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New Orthogonal Designs And Sequences With Two And Three Variables In Order 28, C. Koukouvinos, Jennifer Seberry
New Orthogonal Designs And Sequences With Two And Three Variables In Order 28, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We give new sets of sequences with entries from {0, ±a, ±b, ±c} on the commuting variables a, b, c and zero autocorrelation function. Then we use these sequences to construct some new orthogonal de-signs. We show the necessary conditions for the existence of an OD(28; s1, s2, s3) plus the condition that (s1, s2, s3) ≠ (1,5,20) are sufficient conditions for the existence of an OD(28; s1, s2, s3). We also show the necessary conditions for the existence of an OD(28; s1, s2, s3) constructed using four circulant matrices are sufficient conditions for the existence of 4 — NPAF(s1, …
Necessary And Sufficient Conditions For Three And Four Variable Orthogonal Designs In Order 36, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Necessary And Sufficient Conditions For Three And Four Variable Orthogonal Designs In Order 36, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We use a new algorithm to find new sets of sequences with entries from {0, ±a, ±b, ±c, ±d}, on the commuting variables a, b, c, d, with zero autocorrelation function. Then we use these sequences to construct a series of new three and four variable orthogonal designs in order 36. We show that the necessary conditions plus (.s1, s2, s3, s4) not equal to 12816 18 816 221313 26721 36 816 4889 12825 191313 23 424 289 9 381015 8899 14425 22 916 are sufficient for the existence of an OD(36; s1, s2 s3, s4) constructed using four circulant …
On Amicable Sequences And Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Amicable Sequences And Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
In this paper we give a general theorem which can be used to multiply the length of amicable sequences keeping the amicability property and the type of the sequences. As a consequence we have that if there exist two, four or eight amicable sequences of length m and type (al, a2), (al, a2, a3, a4) or (al, a2, ... , a8) then there exist amicable sequences of length ℓ ≡ 0 (mod m) and of the same type. We also present a theorem that produces a set of 2v amicable sequences from a set of v (not necessary amicable) sequences …
New Weighing Matrices And Orthogonal Designs Constructed Using Two Sequences With Zero Autocorrelation Function - A Review, C. Koukouvinos, Jennifer Seberry
New Weighing Matrices And Orthogonal Designs Constructed Using Two Sequences With Zero Autocorrelation Function - A Review, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
The book, Orthogonal Designs: Quadratic Forms and Hadamard Matrices, Marcel Dekker, New York-Basel, 1979, by A. V. Geramita and Jennifer Seberry, has now been out of print for almost two decades. Many of the results on weighing matrices presented therein have been greatly improved. Here we review the theory, restate some results which are no longer available and expand on the existence of many new weighing matrices and orthogonal designs of order 2n where n is odd. We give a number of new constructions for orthogonal designs. Then using number theory, linear algebra and computer searches we find new weighing …
Some Results On Self-Orthogonal And Self-Dual Codes, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Some Results On Self-Orthogonal And Self-Dual Codes, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We use generator matrices G satisfying GGT = aI+bJ over Zk to obtain linear self-orthogonal and self-dual codes. We give a new family of linear self-orthogonal codes over GF(3) and Z4 and a new family of linear self-dual codes over GF(3).
On Full Orthogonal Designs In Order 72, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Full Orthogonal Designs In Order 72, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We find new full orthogonal designs in order 72 and show that of 2700 possible OD(72; s1, s2, s3, 72—s1—s2—s3) 335 are known, of 432 possible OD(72; s1, s2, 72—si—s2) 308 are known. All possible OD(72; s1, 72 — s1) are known.
Necessary And Sufficient Conditions For Two Variable Orthogonal Designs In Order 44: Addendum, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Necessary And Sufficient Conditions For Two Variable Orthogonal Designs In Order 44: Addendum, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
In our recent paper Necessary and sufficient conditions for some two variable orthogonal designs in order 44, Koukouvinos, Mitrouli and Seberry leave 7 cases unresolved. Using a new algorithm given in our paper A new algorithm for computer searches for orthogonal designs by the present four authors we are able to finally resolve all these cases. This note records that the necessary conditions for the existence of two variable designs constructed using four circulant matrices are sufficient. In particular of 484 potential cases 404 cases have been found, 68 cases do not exist and 12 cases cannot be constructed using …